# LOSSPR

## Description

Probability of loss is a measure of the likelihood that a portfolio will incur a particular percentage of loss at the end of an investment horizon. The function is also able to calculate the within-horizon probability of loss which is estimated as a first-passage time probability.

{% hint style="info" %}
See <https://insights.windhamlabs.com/insights/rethinking-exposure-to-loss> for an introduction to stress testing your portfolios and assessing a more realistic measurement of exposure to loss.
{% endhint %}

## Syntax

The following describes the function signature for use in Microsoft Excel's formula bar.

```excel-formula
=LOSSPR(mu, sigma, horizon, lossThreshold, estWithinHorizon)
```

### Input(s)

| Argument             | Description                                                                                                                                                                          |
| -------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
| **mu**               | Required. Vector / scalar of portfolio return estimate(s).                                                                                                                           |
| **sigma**            | Required. Vector / scalar of portoflio risk estimate(s).                                                                                                                             |
| **horizon**          | Required. Investment time horizon in the same time units of mu and sigma.                                                                                                            |
| **threshold**        | Required. Loss threshold to assess likelihoods.                                                                                                                                      |
| **estWithinHorizon** | Optional. Logical flag (TRUE or FALSE) to indicate whether you would like to calculate the within-horizon risk measurement. If this argument is not specified, it defaults to false. |

### Output(s)

Probability of loss estimate(s).

## Example

![](https://258561627-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MK66-MGuoULhqCDXLwy%2F-MLDa6RQVeSCEx8InW_G%2F-MLDbLMsWQNpZ1zY5cCR%2Fimage.png?alt=media\&token=f3ad9798-0ab4-4d06-bb33-847eb7b21e99)

{% file src="<https://258561627-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MK66-MGuoULhqCDXLwy%2F-MQVB8KBBiZbWQN1Bd4c%2F-MLDbQpbZVBrMJlEQfnG%2FLOSSPR.xlsx?alt=media&token=5b98ddd7-197f-4e43-ad6f-efdff6024b40>" %}
Example Workbook: LOSSPR
{% endfile %}